Abstract

A relationship between orthogonal rational functions and discrete integrable systems is studied by an approach based on Schur-type symmetric functions. A system of orthogonal rational functions is constructed using a multiparameter deformation of the Schur functions. Spectral equations for the orthogonal rational functions are derived by using properties of the Schur-type symmetric functions. The compatibility condition of the spectral equations induces a discrete dressing chain which is a Toda-type discrete integrable system describing dressing transformations for orthogonal rational functions.